Bound state energy E as a function of interaction parameters (a) b ↓ and (b) ε b . In panel (a), the red solid line is the numerical solution of Eq. (5) with the inverse T-matrix being given by Eq. (16), and the blue dashed line is the plot of the approximate solution of Eq. (17). The parameters are chosen as ε b = 0.1 E F and b ↑ = 2.0 . In panel (b), the red solid line represents the energy of the YSR bound state obtained from the numerical solution of Eq. (5), and the blue dashed line is the order parameter ( Δ ), which acts as an indicator of the range of the energy of the YSR bound state. The parameters are chosen to be b ↑ = 3.5 and b ↓ = 1.0 . b ↑ , ↓ are the interaction parameters between the paired atoms and impurity atom, and ε b denotes the strength of the interaction between the paired atoms defined in the main text.